Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part I: stress intensity factor and limit load solutions

The J-integral and the crack opening area are the main parameters required for a leak-before-break evaluation of a piping system. Stress intensity factor and limit load solutions have been widely used for evaluating these parameters in a simplified way. Solutions for the stress intensity factor and limit load for a pipe with a circumferential through-wall crack subjected to axial and bending loads are reviewed and compared in this study. Based on the comparisons, recommendations are then made on expressions for calculating these parameters.     

The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack : Part I: Bending deformation is load-controlled

A net-section stress failure criterion is currently used to determine the critical size of circumferential crack for austenitic stainless steel as used in nuclear reactor piping systems. The acceptable crack size for prescribed applied loadings is determined by assuming that failure occurs when the stress across the net-section (that is the pipe cross-section area reduced by the crack area) attains a critical value, the stress at the cracked section being calculated on the basis of the undeformed pipe configuration. However, an axial compressive load can give an increased bending moment if the stress calculation is based on the deformed pipe configuration. This paper therefore examines the effect of an axial compressive load, superimposed upon a bending load, on the failure of piping due to the presence of a through-wall circumferential crack. The results show that the failure assessment should be based on the deformed configuration even when the axial load is only a small fraction of the pipe's Euler critical load, or otherwise the net-section stress approach can give non-conservative failure predictions.     

Numerical analysis of microwave melting of ice-saturated porous medium filled in a rectangular waveguide with resonator using a combined transfinite interpolation and PDE methods

A numerical study is performed for the melting process of ice-saturated porous medium filled in a rectangular waveguide with a resonator subjected to electromagnetic energy. A microwave system supplies a monochromatic wave in a fundamental mode (TE₁₀ mode) with operating frequency of 2.45 GHz. Focus is placed on establishing a computationally efficient approach for solving moving boundary heat transfer problem in a two-dimensional structured grid. Numerically, preliminary grids are first generated by an algebraic method, based on a transfinite interpolation method, with subsequent refinement using a PDE mapping method. A preliminary case study indicates successful implementation of the numerical procedure. The predicted results from two-dimensional melting model are then validated against available experimental results and subsequently used as a tool for efficient computational prototyping. Based on the numerical results are performed illustrating the influence of resonator and layered configuration, in case of the installed resonator has strongly affected on the microwave power absorbed, temperature distribution, and the melting front during microwave melting process.     

Thermal management and simulation studies of a 200-kW calorimetric dummy load for HE11 mode at 42 GHz

The objective of this study is to design a calorimetric dummy load (CDL) containing an efficient cooling mechanism to absorb maximum power of 200 kW at 42 ± 0.2 GHz frequency for maximum duration of 3 seconds. The design is suited for microwave power propagating in HE₁₁ mode. High microwave power is generally measured and characterized by CDL, which is designed to suit the exiting modes of the gyrotron. In the current project, the output mode of the gyrotron in TE₀₃ is converted to a Gaussian HE₁₁ mode with help of series of mode converters. This study highlights thermal analysis and simulation studies using ANSYS computational fluid dynamics analysis for water coolant passing through helical teflon tubing. Analytical calculations for thermal management of water coolant are also carried out and compared with the simulation studies. A defocusing convex mirror has been designed using a quasi-optical approach. Material selection of the defocusing mirror, based on cost-effectiveness, transient thermal analysis, and microwave power absorption in the skin depth of the material, has been carried out. Finally, a comparison of analytical calculation and simulation studies has been carried out.     

The instability of radial growth of a part-through and part-circumference circumferential crack in a stainless steel pipe subject to bending deformation. Part II—The effect of a superimposed axial compressive load

In the context of the integrity of nuclear reactor piping systems, this paper examines the effect of an axial compressive load, superimposed upon bending loads, on the unstable development of a part-through and part-circumference circumferential crack into a through-wall crack in a stainless steel pipe. Results are obtained for axial compressive stresses up to 20% of the material's yield stress, this being reckoned to be a reasonably large compressive stress level. The results show that if the bending deformation is load-controlled, the failure assessment should be based on the deformed pipe configuration, otherwise the failure predictions will be non-conservative. On the other hand, with displacement-controlled bending deformation an axial compressive stress does not have an adverse effect on crack stability.     

The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack: Part II: Bending deformation is displacement-controlled

In the context of the integrity of nuclear reactor piping systems, this paper examines the effect of an axial compressive load on the instability of growth of a through-wall circumferential crack in a stainless steel pipe that is subjected to displacement-controlled bending deformation. The analytical procedure is based on the deformed pipe configuration, and with the aid of the tearing modulus methodology, the instability criterion is expressed in terms of the magnitude of the compressive load, pipe geometry parameters, and the material's fracture and flow characteristics. The results show that a compressive load can have an adverse effect on crack stability when the axial load is only a small fraction of the pipe's Euler critical load. This conclusion is in general accord with the conclusion for the case where a pipe is subject to load-controlled bending deformation.     

KI–T estimation for embedded flaws in pipes – Part II: Circumferentially oriented cracks

This paper, in parallel to the investigation on axially embedded cracks reported in the companion paper, presents a numerical study on the linear-elastic K_I and T-stress values over the front of elliptical cracks circumferentially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs the interaction-integral approach to compute the linear-elastic stress-intensity factor (SIF) K_I and T-stress values for embedded cracks with practical sizes at different locations in the wall of the pipe. The parametric study covers a wide range of geometric parameters for embedded cracks in the pipe, including: the wall thickness to the inner radius ratio (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). The parametric investigation identifies a significant effect of the remaining ligament length on both the T-stress and K_I values at the crack-front location (denoted by point O) nearest to the outer surface of the pipe and at the crack-front location (denoted by point I) nearest to the inner surface of the pipe. The numerical investigation establishes the database to derive approximate functions from a nonlinear curve-fitting procedure to predict the T-stress and K_I values at three critical front locations of the circumferentially embedded crack in a pipe: points O, I and M. The proposed T-stress and K_I functions utilize a combined second-order polynomial and a power-law expression, which presents a close agreement with the T-stress and K_I values computed from the very detailed finite element models. The comparison between the circumferentially embedded crack and the axially embedded crack indicates that both the T-stress and K_I values at crack-front points O and I in a circumferential crack equal approximately 50% the T-stress and K_I values at the corresponding front locations in an axial crack with the same crack depth ratio, the same crack aspect ratio and the same pipe wall thickness to the inner radius ratio.     

The effect of an axial compressive load on the stability of a circumferential crack in a stainless steel pipe that is built-in at both ends

Against the background of the integrity of boiling water reactor piping systems, this paper investigates the effect of an axial compressive load on the stability of a circumferential crack in a stainless steel pipe that is built-in at both ends. One end is fixed, while the other, though allowed to move in an axial direction, is subject to a transverse displacement, and crack instability is examined when this displacement is fixed. The circumferential instability of a through-wall crack and the radial instability of a part-through and part-circumference crack are both examined. For both types of instability, it is shown that a compressive load has an adverse influence on crack stability only when the compressive load is a large fraction (>0·5) of the Euler critical load.     

KI–T estimations for embedded flaws in pipes – Part I: Axially oriented cracks

This study reports a numerical investigation on the linear-elastic K_I and T-stress values over the front of elliptical cracks axially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs an interaction integral approach to compute the linear-elastic stress intensity factor (SIF) K_I and T-stress values from very detailed crack-front meshes. The verification study confirms the accuracy of the adopted numerical procedure in computing the K_I values based on existing results for external axial surface cracks in the wall of a cylindrical structure. The parametric investigation covers a wide range of geometric parameters including: the wall thickness to the inner radius ratio of the pipe (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the crack location measured by the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). Subsequent efforts develop, from a nonlinear curve-fitting procedure, a new set of equations to estimate the T-stress and K_I values at three critical front locations of the axial elliptical cracks: the crack-front point O nearest to the outer surface of the pipe, the crack-front point I nearest to the inner surface of the pipe and the crack-front point M on the centerline of the axial crack. These equations combine a second-order polynomial with a power-law expression to predict the pronounced variations in the T-stress and K_I values with respect to the geometric parameters. The coefficients of the new K_I and T-stress equations either take a constant value or incorporate the linear variation with respect to the pipe wall thickness over the inner radius ratio, t/R_i. The proposed equations demonstrate a close agreement with the finite element (FE) results, which indicate very strong dependence of the T-stress and K_I values at point O and point I on the corresponding ligament lengths, e_O and e_I.     

The inhibitory effect of carbon monoxide contained in hydrogen gas environment on hydrogen-accelerated fatigue crack growth and its loading frequency dependency

The effect of carbon monoxide (CO) contained in H₂ gas as an impurity on the hydrogen-accelerated fatigue crack growth of A333 pipe steel was studied in association with loading frequency dependency. The addition of CO to H₂ gas inhibited the accelerated fatigue crack growth due to the hydrogen. The inhibitory effect was affected by the CO content in the H₂ gas, loading frequency, and crack growth rate. Based on these results, it was revealed that the inhibitory effect of CO was governed by both competition between the rate of fresh surface creation by the crack growth and the rate of coverage of the surface by CO and time for hydrogen diffusion in the material to the crack tip with reduced hydrogen entry by CO.     

The stability of crack growth in pipes subject to tensile loads

This paper presents a simple analysis for the stability of crack growth in 304 stainless steel pipes subject to tensile loads. The model of two identical part-through and part-circumference cracks, symmetrically situated with regard to the pipe cross-section, is examined for crack stability under displacement control tensile loading. Irrespective of the crack depth, the instability condition for a wide range of crack lengths, i.e. except for very short cracks and long cracks, is: $\text{2σ}{}_0\text{L}\text{πER}{}_{\mathrm{\chi }}\text{≡}\text{2L}\text{πR}\text{·}\text{1}\text{T}{}_{\mathrm{MAT}}\text{> 1}$ where σ₀ is the flow stress, E is Young's modulus, L is the pipe length, R is the pipe radius, χ is the crack tip opening angle, CTOA, associated with the crack growth and T_MAT is the material's tearing modulus. With a CTOA of 20° (i.e. T_MAT ～ 200), $\text{L}\text{R}$ must exceed 300 for instability. Since this number is far in excess of the $\text{L}\text{R}$ values for typical piping systems, the stability of cracks in pipes subject to tensile loads is essentially demonstrated.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part III: estimation of crack opening area

Evaluation of the crack opening area (COA) plays a central role in the evaluation of the critical crack length for a detectable leak for piping systems. Simplified evaluation methods for the COA for a circumferential through-wall crack in a pipe subjected to axial and bending loading or their combination is reviewed in this paper. Elastic solutions are compared and recommendations are given. Plastic solutions by the reference stress method are compared with nonlinear finite element solutions. The reference stress method tends to overestimate the COA for medium or large crack angles. Considerable improvement is achieved by making empirical modifications to the limit load expressions used in the calculation of the reference stress.     

核电站高中能管道断管影响探讨

在设计核电站时,须对安全壳内外的高能与中能管道进行发生假想性断管事件及其后续效应的设计分析。这些管道一旦发生破裂,泄漏的高能量流体将对管道施加很大的横向力,使管道产生高速运动,即管道甩动。这种高速运动的管道可能会对周围结构造成严重破坏,因而引起世界上各主要发展核电国家的重视,并开展了大量的研究工作。详细叙述常规岛侧高中能管道断管位置的判定准则、假想破口的类型、断管的后续影响及其防护等。还进一步介绍有关管道断裂甩动问题的各种计算方法,如力矩平衡法、能量平衡法、有限元法等。     

Microwave heating of saturated packed bed using a rectangular waveguide (TE10 mode): Influence of particle size,sample dimension,frequency, and placement inside the guide

This paper presents the numerical and experimental analysis of microwave heating in a saturated packed bed by using a rectangular waveguide (TE₁₀ mode). A complete mathematical model is proposed, which uses comprehensive two-dimensional energy and momentum equations to describe unsteady temperature and flow fields, coupled with a complete solution of the transient Maxwell’s equations in time domain. The influences of particle size, sample dimension, placement inside the guide, and frequency on heat transfer and flow patter are studied. The simulation results are in good agreement with experimental data. Flow pattern strongly depends on the bead size and thermal efficiency of the sample changes with sample size and frequency. Furthermore, the middle placed inside the guide aids in uniform heating.     

Predictions for fatigue crack growth life of cracked pipes and pipe welds using RMS SIF approach and experimental validation

The objective of the present study is to understand the fatigue crack growth behavior in austenitic stainless steel pipes and pipe welds by carrying out analysis/predictions and experiments. The Paris law has been used for the prediction of fatigue crack growth life. To carry out the analysis, Paris constants have been determined for pipe (base) and pipe weld materials by using Compact Tension (CT) specimens machined from the actual pipe/pipe weld. Analyses have been carried out to predict the fatigue crack growth life of the austenitic stainless steel pipes/pipes welds having part through cracks on the outer surface. In the analyses, Stress Intensity Factors (K) have been evaluated through two different schemes. The first scheme considers the ‘K’ evaluations at two points of the crack front i.e. maximum crack depth and crack tip at the outer surface. The second scheme accounts for the area averaged root mean square stress intensity factor (K_RMS) at deepest and surface points. Crack growth and the crack shape with loading cycles have been evaluated. In order to validate the analytical procedure/results, experiments have been carried out on full scale pipe and pipe welds with part through circumferential crack. Fatigue crack growth life evaluated using both schemes have been compared with experimental results. Use of stress intensity factor (K_RMS) evaluated using second scheme gives better fatigue crack growth life prediction compared to that of first scheme. Fatigue crack growth in pipe weld (Gas Tungsten Arc Welding) can be predicted well using Paris constants of base material but prediction is non-conservative for pipe weld (Shielded Metal Arc Welding). Further, predictions using fatigue crack growth rate curve of ASME produces conservative results for pipe and GTAW pipe welds and comparable results for SMAW pipe welds.     

Leak-before-break qualification of primary heat transport piping of 500 MWe Tarapur atomic power plant

The advent of Leak-Before-Break (LBB) concept has now replaced the traditional design basis event of the Double-Ended-Guillotine-Break (DEGB) to design the Primary Heat Transport (PHT) system piping of the Pressurised Heavy Water Reactor (PHWR) and Pressurised Water Reactor (PWR). This approach is being adopted to design the PHT system piping of 500 MWe Indian PHWR to be built at Tarapur (Tarapur Atomic Power Plant 3 and 4). The LBB concept basically demonstrates through fracture mechanics analysis that there is negligible chance of any catastrophic break of PHT pipes without prior indication of leakage. There are several steps in this work of LBB qualification, namely, evaluation of loads on the piping components, generation of tensile and fracture properties of PHT pipe base and weld material, determination of leakage size crack (LSC) and the elastic–plastic fracture mechanics (EPFM) and limit load analysis of the piping components with postulated LSC to evaluate the critical load at unstable ductile tearing and the limit load, respectively. The paper deals with the fracture analysis of the straight pipes and elbows of three pipe lines in the PHT system of TAPP 3 and 4. Three crack configurations are considered in the analysis. These are throughwall circumferential crack at the weld location of straight pipe and extrados of the elbow and throughwall axial crack at the elbow crown. In all the cases, necessary factor of safety with respect to the anticipated safe shutdown earthquake (SSE) load and LSC are shown to be more than the minimum required values for LBB qualification.     

The J-resistance curve leak-before-break test program on material for the darlington nuclear generating station

The Darlington Leak-Before-Break (DLBB) approach has been developed for large diameter (21, 22, 24 inch) SA106B heat transport (HT) piping and SA105 fittings as a design alternative to pipewhip restraints and in recognition of the questionable benefits of providing such restraints. Ontario Hydro's DLBB approach is based on the elastic plastic fracture mechanics (EPFM) method. In this test program, J-resistance curves were determined from actual pipe heats that were used in the construction of the Darlington heat transport systems (Units 1 and 2). Test blocks were prepared using four different welding procedures for nuclear Class I piping.

The test program was designed to take into account the effect of various factors such as test temperature, crack plane orientation, welding effects, etc., which have influence on fracture properties. A total of 91 tests were conducted. An acceptable lower bound J-resistance curve for the piping steels was obtained by machining maximum thickness specimens from the pipes and by testing side grooved compact tension specimens.

Test results showed that all pipes, welds and heat-affected zone materials within the scope of the DLBB program exhibited uppershelf toughness behaviour. All specimens showed high crack initiation toughness J_Ic, rising J-resistance curve and stable and ductile crack extension. Toughness of product forms depended on the direction of crack extension (circumferential versus axial crack orientation). Toughness of DLBB welds and parent materials at 250°C was lower than that at 20°C.     

Allowable sizes of axial flaws in pressurized pipes made of moderate toughness materials

Failure stresses for axially part-through flawed pipes made of moderately tough materials are predicted by several fracture mechanics. However, allowable flaw sizes using these fracture mechanics cannot be simply described because there are many effective parameters such as pipe diameter, wall thickness, material properties, etc. To establish codes and standards to evaluate flaws for piping of light water reactors, we determine unified allowable sizes for axial flaws in pipes subjected to internal pressure from J-integral based fracture mechanics. The allowable sizes are simply tabulated using a single parameter which consists of pipe geometry and material properties.     

Leak-before-break application in US light water reactor balance-of-plant piping

This paper describes the criteria and methodology for a leak-before-break (LBB) program for high energy balance-of-plant (BOP) nuclear piping in the United States. LBB, the analytical demonstration that high toughness piping will leak detectably before catastrophic failure, can be applied to any operational or pre-operational light water reactor plant to minimize pipe rupture hardware and to discount pipe rupture dynamic effects.

The general methodology described herein, encompasses applicable US NRC regulatory requirements and incorporates experience gained in the licensing process of actual LBB programs. First, candidate piping systems must be carefully screened to verify that they are not subject to failure by phenomena that would adversely affect the accurate evaluation of flaws. Next, pipe stresses, material properties, and leak detection capabilities are gathered for the fracture mechanics and fluid mechanics analyses. At the piping locations which have the least favorable combination of material properties and stress, a crack is postulated which is of sufficient size that the resulting leakage will be detected by installed leak detection systems. Finally, LBB is demonstrated if the postulated crack remains stable even if a seismic event takes place before the crack is discovered and repaired. An LBB example is presented in this paper for a generic pressurizer surge line, and reflects the consideration of flow stratification on LBB analyses.